Isospectrality of spherical MHD dynamo operators: pseudo-Hermiticity and a no-go theorem

The isospectrality problem is studied for the operator of the spherical hydromagnetic alpha^2-dynamo. It is shown that this operator is formally pseudo-Hermitian (J-symmetric) and lives in a Krein space. Based on the J-symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the alpha^2-dynamo operator matrix. An intrinsic structural inconsistency is obtained in the set of associated matrix Riccati equations. This inconsistency is interpreted as a no-go theorem which forbids the construction of isospectral alpha^2-dynamo operator classes with the help of first-order differential intertwining operators.Comment: 13 pages, LaTeX2e, improved references, to appear in J. Math. Phy

Embeddings of SL(2,Z) into the Cremona group

Geometric and dynamic properties of embeddings of SL(2,Z) into the Cremona group are studied. Infinitely many non-conjugate embeddings which preserve the type (i.e. which send elliptic, parabolic and hyperbolic elements onto elements of the same type) are provided. The existence of infinitely many non-conjugate elliptic, parabolic and hyperbolic embeddings is also shown. In particular, a group G of automorphisms of a smooth surface S obtained by blowing-up 10 points of the complex projective plane is given. The group G is isomorphic to SL(2,Z), preserves an elliptic curve and all its elements of infinite order are hyperbolic.Comment: to appear in Transformation Group

Sur les exposants de Lyapounov des applications meromorphes

Let f be a dominating meromorphic self-map of a compact Kahler manifold. We give an inequality for the Lyapounov exponents of some ergodic measures of f using the metric entropy and the dynamical degrees of f. We deduce the hyperbolicity of some measures.Comment: 27 pages, paper in french, final version: to appear in Inventiones Mat

On a Sturm-Liouville Type Problem with Retarded Argument

In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.Comment: 15 page

Approximation by Entire Functions on Unbounded Domains in Cn

AbstractGiven a function analytic in an unbounded domain of Cn with certain estimates of growth, we construct an entire function approximating it with a certain rate in some inner domain and give estimates of growth of the approximating function. This extends well-known results of M. V. Keldysh to several variables and more general domains

The theory of V-Bezoutians and its applications

AbstractSome propositions of the theory of V-Bezoutians are presented. As an application the following problem is considered: to construct an appropriate Pontryagin space in which a given matrix boundary value problem (containing the eigenvalue parameter in the boundary conditions) is self-adjoint. The solution of this problem is given (in three special cases) with the help of V-Bezoutians of matrix polynomials entering the boundary conditions

Quasi-Sampling Sets for Analytic Functions in a Cone

AbstractWe study analogues of sampling sets for analytic functions in cones ofCn. Cartwright-type and Bernstein-type theorems, previously known only for functions of exponential type inCn, are extended to the case of functions of arbitrary order in a cone